Question: The drama club sold bags of candy and cookies to raise money for the spring show. Bags of candy cost $$5.50$, and bags of cookies cost $$4.50$, and sales equaled $$56.00$ in total. There were $8$ more bags of cookies than candy sold. Find the number of bags of candy and cookies sold by the drama club.
Let $x$ equal the number of bags of candy and $y$ equal the number of bags of cookies. The system of equations is then: ${5.5x+4.5y = 56}$ ${y = x+8}$ Since we already have solved for $y$ in terms of $x$ , we can use substitution to solve for $x$ and $y$ Substitute ${x+8}$ for $y$ in the first equation. ${5.5x + 4.5}{(x+8)}{= 56}$ Simplify and solve for $x$ $ 5.5x+4.5x + 36 = 56 $ $ 10x+36 = 56 $ $ 10x = 20 $ $ x = \dfrac{20}{10} $ ${x = 2}$ Now that you know ${x = 2}$ , plug it back into $ {y = x+8}$ to find $y$ ${y = }{(2)}{ + 8}$ ${y = 10}$ You can also plug ${x = 2}$ into $ {5.5x+4.5y = 56}$ and get the same answer for $y$ ${5.5}{(2)}{ + 4.5y = 56}$ ${y = 10}$ $2$ bags of candy and $10$ bags of cookies were sold.